Thin Film Interference
What is a thin film?
A thin film is a thin layer of material that has a
different index of refraction than its surroundings.
Thin films cause incident light to undergo interference
(constructive or destructive, depending on the
wavelength of the light and the thickness of the film).
Thin film interference is responsible for all of the colors
that appear in soap bubbles and oil slicks.
When light is incident on a thin film,
part of the incident light is reflected off of the top
of the film, and part is transmitted into the film
and reflected off of the bottom!
air
soap
air
It is the interference of
these two reflected rays
that we will see when
we look into the film.
t = thickness of the film
In reality, the light makes many, many reflections in the film!
t
However, we only need to analyze the first two reflected rays
in order to make predictions about the interference pattern.
There are two types of thin films
Type I: Oil slick type (fast-slow-slower)
low n
air
high n
oil
higher n
ground
Type II: Bubble type (fast-slow-fast)
low n
air
high n
soap
low n
air
Type I: Oil Slick Type
1
Light is incident upon the oil from
the air. It is partially transmitted
into the oil, and partially reflected
back into the air.
2
air
(n = 1.0)
t
oil
(n ≈ 1.5)
ground
(very high n)
The light in the oil reflects off of
the ground, and refracts back out
into the air.
As a result, we have multiple rays
coming toward our eyes that started
from the same incident ray!
The most important concept of thin film inteference
1
2
air
(n = 1.0)
t
oil
(n ≈ 1.5)
ground
(very high n)
If rays 1 and 2 are in phase with
one another, then there will be
constructive interference. You will
be able to see that wavelength of
light from the surface of the film.
If rays 1 and 2 are out of phase with
one another, then there will be
destructive interference. You will
not be able to see the wavelength of
light from the surface of the film.
The waves start out in phase, but travel different
path lengths by the time that they are superimposed
Wave 2 travels an extra distance of ≈ 2t!
1
2
air
(n = 1.0)
t
oil
(n ≈ 1.5)
ground
(very high n)
However…
air
(n = 1.0)
oil
(n ≈ 1.5)
when a wave (even light) is
reflected off of a different
medium, it may invert,
depending on the density of
the medium! Let’s review
how this works.
Boundary Reflections: Revisited
When a wave reflects off of a more dense medium than
the one in which it is traveling, it will become inverted.
This is called a 180° phase change.
This same principle applies to light reflecting off of a
medium with a higher refractive index.
Less dense
More dense
180° phase flip – trough becomes a crest, or vice
versa
Type I Thin Films: Oil Slick
1
2
air
(n = 1.0)
t
oil
(n ≈ 1.5)
ground
(very high n)
At which interface(s) does the reflecting light undergo a phase flip?
At which interface(s) does the reflecting light undergo a phase flip?
At both!
When the light reflects off of
the oil from the air, it is phase
flipped.
When the transmitted ray
reflects off of the ground at
the bottom of the oil, it is also
phase flipped!
1
2
air
(n = 1.0)
oil
(n ≈ 1.5)
ground
(very high n)
Since both of the waves that are interfering have undergone a 180°
phase flip, the net result is the same as if neither of the waves did!
A summary so far
1
The waves start out in phase.
2
air
(n = 1.0)
t
oil
(n ≈ 1.5)
ground
(very high n)
Both parts undergo phase
flips at some point (so it is
mathematically the same as if
neither one did).
Wave 2 travels an extra
distance of ≈ 2t
And now for the grand finale
The waves started out in phase, but one of them went some extra distance.
In order for them to constructively interfere, they must be back in phase when
they are superimposed.
Does this sound familiar?
Constructive interference must satisfy the equation
L1 - L2 = ml
Where L1 is the distance traveled by the wave reflected off of the top of the film,
and L2 is the distance traveled by the wave reflected off of the bottom of the film
m = 0 if the waves have traveled the same distance, m = 1 if one of the waves has traveled
one extra wavelength, m = 2 if one of the waves have traveled two extra wavelengths, etc.
The end result!
Wave 2 has traveled an extra
distance of ≈ 2t.
1
2
This gives the end result
t
2t = ml
for constructive interference
in a type I thin film.
And, for destructive interference…
2t = (m- 1 2)l
in a Type I thin film (low-high-higher)